Controlled K-g-fusion frames in Hilbert C*-modules

TL;DR

This paper introduces controlled g-fusion frames and controlled K-g-fusion frames in Hilbert C*-modules, exploring their properties, perturbation issues, and providing examples to demonstrate their applications.

Contribution

It is the first to define and analyze controlled g-fusion frames and controlled K-g-fusion frames within Hilbert C*-modules, including their properties and perturbation behavior.

Findings

Defined controlled g-fusion and K-g-fusion frames in Hilbert C*-modules.

Analyzed properties and perturbation of these frames.

Provided illustrative examples supporting the theoretical results.

Abstract

Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g-fusion frame and controlled K-g-fusion frame in Hilbert C*-modules and we give some properties. Also, we study the pertubation problem of controlled K-g-fusion frame. Moreover, an illustrative examples is presented to support the obtained results.